Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
1.0k views
in Binomial theorem by (52.7k points)

The sides of a right-angled triangle are in arithmetic progression. If the triangle has area 24, then what is the length of its smallest side?

1 Answer

0 votes
by (46.6k points)
selected by
 
Best answer

Let a be the first term and d be the common difference, then the sides of triangle are a, a + d and a + 2d.

Area of triangle = 1/2 x Base x Height

Substituting the values, we get

a(a + d) = 2 x 24 

a(a + d) = 48    ....(1)

Applying Pythagoras theorem, we get

From Eq. (1), we know that a + d ≠ 0. Therefore,

3d - a = 0 ⇒ 3d = a

Substituting in Eq. (1), we get

3d(3d + d) = 48

⇒ 3d x 4d = 48

⇒ d2 = 48/12 ⇒ d2 = 4 ⇒ d = 2

From 3d = a, we get

a = 2 x 3 = 6 ⇒ a = 6

Therefore, the sides of the triangle are 6, (6 + 2), (6 + 2 x 2), that is, 6, 8, 10.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

...